Verse 2.3: O son of Pṛthā, do not yield to this degrading impotence. It does not become you. Give up such petty weakness of heart and arise, O chastiser of the enemy.
Weakness of heart tends to get in the way of doing our duty. I recognize this everyday. The moment you commit to something, immediately you are tested. To give a small but illustrative example, my intention and personal promise has been to write something on a verse of the Gita everyday (notwithstanding severe illness). However, almost everyday I have to fight to keep this mini-vow. Sure, there are days when I'm actually "itching to read and write" but normally, not so much.
Similarly, we have a duty to respect each and every living entity, but sometimes it can be difficult. Although we may not like it, a spider or ant has just as much a right to inhabit the space we occupy as we do. But we don't recognize this very often. The reason for that is weakness of heart.
Weakness of heart is a very broad subject, but here I'd like to focus on lack of determination and proper guidance. If one is not guided properly, it is very easy to be swayed. I see this all the time in the practice of bhakti yoga. My spiritual mentors and role models have all been guided so expertly in their own cultivation of bhakti that nothing can stray them from the path. Hence, when I interact with them, I constantly feel inspired and enthused. I also feel my own faith grow tremendously. However, those who like to "do what the spirit moves them" are often easily won over by different philosophies, ideas and honeyed words. That is why I always try to remind myself of one of my favourite phrases from the Gita speaks on this point directly, "One's associations and ambitions develop according to the company one keeps."
With that guidance automatically comes focus. If cannot stand up for and believe in our convictions then its is very easy to be unfocused. Conviction brings about focus because it allows the path to become clear.
In this material world we live in, the two prevalent things we encounter is a lack of proper guidance and a lack of proper focus. Here we see Arjuna undergoing the same confusion we experience (often daily!). Arjuna is not sure what the proper path is to take and hence he doesn't know what to do.
So, we can all learn from Arjuna how to defeat these petty weaknesses of heart. We too can ask for guidance from a bona fide and authoritative source (i.e. the bhakti yogi who walks the talk) and ask for encouragement and support so that we too may become convinced and focused to do the right thing.